Hi Lynn,
First of all, I would like to thank you for your PERFECT blog. It is so helpful.
I used used to write "We will be sending the XYZ report next Sunday (26th of June)". Is it correct or I should write it as (June 26)

Lynn, I have just connected to your business writing blog and I have immediately started learning things from this very first attempt. Thank you for teaching so many users of this blog, with your wisdom of knowledge.

How can I politely correct my boss when she writes dates like this: 6/11th? It drives me crazy. Please help! I've all but given up on correcting dates otherwise, since it seems everyone, including marketing, advertisement, publishing, has accepted writing dates such as June 11th, 2014 as standard. So disappointing.

Then invite your boss to read the blog post with you. Ask her, "How can we get everyone to render dates correctly?" She may not believe my blog post, but you can present to her ANY reputable style manual or style section of a dictionary. She can't argue with 100 percent of experts.